SOLUTION: find all real values of θ in the interval [0°,360°) that satisfy the equation 4sin^4θ - 5sin^2θ+1=0.

Algebra ->  Trigonometry-basics -> SOLUTION: find all real values of θ in the interval [0°,360°) that satisfy the equation 4sin^4θ - 5sin^2θ+1=0.      Log On


   

Question 759939: find all real values of θ in the interval [0°,360°) that satisfy the equation
4sin^4θ - 5sin^2θ+1=0.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
find all real values of θ in the interval [0°,360°) that satisfy the equation
4sin^4θ - 5sin^2θ+1=0.
4sin%5E4%28x%29-5sin%5E2%28x%29%2B1=0
let u=sin^2(x)
u^2=sin^4(x)
..
4u^2-5u+1=0
(4u-1)(u-1)=0
..
u=1=sin^2(x)
sin(x)=±1
x=90º, 270º
..
u=1/4=sin^2(x)
sin(x)=±1/2
x=π/6, 5π/6, 7π/6, 11π/6